Explanation The sketch of the solid obtained by rotation is determined and then we use the Shell Method to obtain its volume after calculating its height and radius. Given: f ( x ) = x x 3 + 1 over the interval [ 1 , 4 ] . Calculation: The sketch of the solid obtained is shown below: The shell has radius x and height x x 3 + 1 therefore the volume of the solid is given by 2 π ∫ 1 4 x ( x x 3 + 1 ) d x ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.4, Problem 6E

To determine

To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the $y$ -axis and also find its volume.

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Chapter 6.4, Problem 5E

Chapter 6.4, Problem 7E

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Chapter 6 Solutions

Calculus - Standalone book

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the y -axis and also find its volume.

Solution Summary: The author explains how the sketch of the solid obtained by rotation is determined and then uses the Shell Method to obtain its volume.

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To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the $y$ -axis and also find its volume.

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Chapter 6 Solutions

To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the y -axis and also find its volume.

Solution Summary: The author explains how the sketch of the solid obtained by rotation is determined and then uses the Shell Method to obtain its volume.

Concept explainers

Videos

To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the y-axis and also find its volume.

Want to see the full answer?

Chapter 6 Solutions

To sketch the solid obtained by rotating the region underneath the graph of the function over the given interval about the $y$ -axis and also find its volume.